Hi wibble; If you still have the Puppy ISO file you downloaded, that`s all you need.
If you want to you can copy the Puppy dir. to the HD, this will save the Save file also.

You don`t say how you`re booting Puppy, I assume with a grub, but maybe syslinux.
Both can boot multiple Puppies on HD or USB.
Copy the FatDog files to a dir. on the USB, just like Puppy-5.6.1.
Then open the boot config. file ( menu.lst for grub, or syslinux.cfg ) in Geany editor.
Copy the lines for Puppy-5.6.1 making 2 sets of them, and edit the second set.
Change all the precise5.6.1 paths to FatDog paths and change the ID line too.

This is kind of confusing I know... Post your boot config. file and I`ll modify it for you.
Also, say what you named the dir. that FatDog is in.

I think the mirror is usually for partition backup, like backing up the USB`s whole partition.

Flash is correct, but I don`t know if backing up the Save file every shutdown is needed.
The Save file is changed with config. changes and added or removed PET packages.
That`s why I always use SFS package files, or DirApp or RoxApp packages, they don`t take up the Save file space.

So backing up the Save file every now and then is good, you can restore to close to the current setup.
USB flash drives run in ram so as to not wear them out, so they auto.-backup every shutdown.

### Boot managers:
If the flash drive has a menu.lst file in it`s root or in /boot, then the manager is grub2 or grub4dos.
If there`s a syslinux.cfg or extlinux.cfg file in the drive`s root or in /boot, then the manager is syslinux.

### Also of interest... What is the flash drive formatted to: ext2-3-4, fat, or ntfs.
.

Remember...
When you restore your PupSaveHotBackup of the pupsave file...
After deleting the old copy...
And restoring the backup copy...
You will need to edit the name of the restored copy to remove the extra stuff on the end of the name, so it has the same name as had the original.

See below my screenshot of my backup [on the right], and the original [in the middle].

"X File Explorer" [Xfe] is the file explorer displaying the files shown below, and used to make the screenshot.
It has twin file panes to the right, plus a folder hierarchy pane on the left.
The twin panes can be used to "Copy to..." from one pane to the other.

wibble; Only one default line is allowed, it`s what boots if a menu selection is not made.
It sets the "label" line to boot after the "timeout" seconds have passed.
And your "initrd=" line has the path in the wrong place.
The first 2 paragraphs are generic and only need to be in the file one time.
"timeout" is pretty long at 50 seconds, I use 7 seconds, plenty of time to select the menu.
"kernel" and "append" lines are the boot instructions.
Puppy has many boot options, you should look at them to become familiar with them.
# P.S. I used fatdog64 for the path folder, try to make them complete so they won`t interfere with each other.
A version number on the fatdog folder ( like the precise-5.6.1 folder below ) would be a good idea too.